What resources or analogies helped you visualize linear algebra for ML?

[Andrew14]

I'm an undergraduate computer science student taking a required linear algebra course, and while I understand the mechanical steps for operations like matrix multiplication and finding determinants, I'm struggling to grasp the deeper geometric intuition behind concepts like eigenvectors and vector spaces. This is becoming a problem as I start my machine learning elective, where these ideas are foundational. For students or professionals who overcame a similar hurdle, what resources or analogies helped you visualize and truly understand the applications of linear algebra beyond just solving textbook problems?

[Anthony77]

You're not alone. A good starting image is a rubber-sheet warp: a linear transform reshapes space, and eigenvectors are the directions that only stretch or compress—no rotation. The eigenvalue is how strong that stretch is.

[Jonathan_S]

Two anchors I’d point you to: 3Blue1Brown's Essence of Linear Algebra (especially the eigen stuff) and MIT OpenCourseWare’s Linear Algebra course (Strang). For more practice, Khan Academy covers basics, and Andrew Ng’s ML course notes tie the math to PCA/SVD nicely.

[Brian77]

A handy analogy: think of vector spaces as all possible lines through the origin. A basis gives you a coordinate frame, and eigenvectors are the special directions that survive the transform unchanged in direction, only scaled.

[Tyler_W]

In ML terms, eigenvectors underpin PCA. You rotate data into the eigenbasis so the covariance matrix is diagonal, and the top eigenvectors capture the most variance. That’s the intuitive link big enough to ground your machine learning work.

[EvelynR]

A practical 4-week plan: Week 1 – vector spaces, spans, bases; Week 2 – eigenvectors/eigenvalues with simple 2×2 examples; Week 3 – orthogonality, projections, Gram-Schmidt; Week 4 – connect to ML with PCA/SVD and a tiny Python exercise to compute eigenvectors. 20–30 minutes a day keeps it doable.

[NoraG]

Quick check-in: do you prefer visual/video explanations or more formal proofs? If you share your preferred style, I can tailor a 1-week micro-syllabus with links and small exercises.